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Find tan(t) ,sin(t) when cos(t)= -3/5

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If cos(t)= -3/5  and t is in Quadrant III, find

a) sin(t)

b) tan(t)

asked Jun 20, 2013 in TRIGONOMETRY by skylar Apprentice

1 Answer

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Given that cos(t) = -3/5

a) sin(t)

Then sin2(t) + cos2(t) = 1

Substitute cos(t) value

sin2(t)+ ( -3/5)2= 1

sin2(t) = 1- 9/25

sin(t) = √ 16/25

Therefore sin(t) = 4/5

b) tan(t)

tan(t)  = sin(t)/cos(t)

(4/5)/(-3/5) = - 4/3

Therefore tan(t) = - 4/3

Therefore sin(t) = 4/5 and tan(t) = -4/3.

 

 

answered Jun 20, 2013 by goushi Pupil

The value of sin(θ) is negative and tan(θ) is positive in third quadrant.

Therefore, sin(t) = - 4/5 and tan(t) = 4/3.

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